A note on $q$-truncated exponential polynomials

Abstract

In this paper, we introduce the $q$-truncated exponential polynomials by means of the integral form. Certain properties of the $q$-truncated exponential polynomials like series definition, recurrence relations, $q$-differential equations and integral representations are obtained. Also, we introduce the associated $q$-truncated exponential polynomials, higher order $q$-truncated exponential polynomials and higher order associated $q$-truncated exponential polynomials. Furthermore, we obtain their integral forms, generating functions, series definitions, summation and operational formulas.